Information on Result #696933
Linear OA(3225, 32783, F32, 8) (dual of [32783, 32758, 9]-code), using construction X applied to Ce(7) ⊂ Ce(3) based on
- linear OA(3222, 32768, F32, 8) (dual of [32768, 32746, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(3210, 32768, F32, 4) (dual of [32768, 32758, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(323, 15, F32, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,32) or 15-cap in PG(2,32)), using
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- Reed–Solomon code RS(29,32) [i]
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3225, 32783, F32, 2, 8) (dual of [(32783, 2), 65541, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (17, 25, 32783)-net over F32 | [i] | ||
| 3 | Linear OOA(3225, 16391, F32, 2, 8) (dual of [(16391, 2), 32757, 9]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3225, 8195, F32, 8, 8) (dual of [(8195, 8), 65535, 9]-NRT-code) | [i] | OA Folding and Stacking | |